# Cylindrical Hall Thruster (cylHallThrusterT.pre)

Keywords:

electric propulsion, Hall thruster channel, erosion models.

## Problem description

Electric Hall thrusters are used for in-space propulsion and satellite station-keeping needs. The discharge plasma inside the Hall thruster channel is produced by the ionization of electrons with a neutral propellant gas such as xenon. The electrons are emitted from the neutralizer cathode placed at the exit of the Hall thruster (cathode end). The neutral gas is fed into the channel from the anode end of the Hall thruster channel. The electrons are confined inside the Hall thruster channel by the radial magnetic field applied through the solenoidal magnetic fields. Plasma xenon ions are accelerated out of the channel at high velocity, which produces the thrust necessary for space propulsion. Recently these thrusters are being designed to support long lifetime, high-power and high-thrust operations. The channel wall erosion occurring inside of the Hall thruster is one of the main limitations to these design needs. It is important to understand the plasma discharge processes occurring inside the Hall thruster channel to predict the lifetime of the Hall thruster based on the calculations of sputtered material from the Hall thruster channel.

This example demonstrates the xenon discharge plasma processes of a Stationary Plasma Thruster (SPT-100) channel. The outer cylinder has a radius of 5 cm and the inner cylinder has a radius of 3.5 cm. The radial channel gap is 1.5 cm. The channel length is 2.5 cm and the simulation domain extends 1 cm outside the channel region (to simulate both the channel and the plume plasma). The anode on the left wall is biased to 300 V. Both inner and outer cylinders are modeled as dielectric cylinders (with hexagonal boron-nitride dielectric material coating) with a dielectric permittivity ratio of 4.6. The exit boundary is set to 0 V. An electron source is placed at the channel exit to simulate electron emission from the neutralizer cathode and the cathode emission current is set to 4.5 A. Neutral xenon gas is modeled as a static fluid background. The neutral gas density is set to be linearly decreasing with a maximum gas density at the anode end of the channel. The simulation is initiated from a uniform plasma with both electrons and xenon ions. Self-similar scaling system laws for the simulation of Hall thruster channel are enabled as described by Figure 1 in [MCL+11]. This is based on earlier work by Taccogna [TLCS04][TLCS05]. The scale factor is set to 1/50, i.e., the thruster dimensions are scaled by 1/50. This scaling is followed so that the kinetic Hall thruster channel plasma simulations can be performed in a reasonable run time. The scaling affects the physical dimensions and external potentials.

This simulation can be performed with a VSimPD license.

## Opening the Simulation

The cylindrical Hall thruster example is accessed from within VSimComposer by the following actions:

• In the resulting Examples window expand the VSim for Plasma Discharges option.
• Expand the Spacecraft (text-based setup) option.
• Select “Cylindrical Hall Thruster (text-based setup)” and press the Choose button.
• In the resulting dialog, create a New Folder if desired, and press the Save button to create a copy of this example.

The basic variables of this problem should now be alterable via the text boxes in the left pane of the Setup pane, as shown in Fig. 532.

Fig. 532 Setup Window for the Cylindrical Hall Thruster Channel example.

## Input File Features

The input file allows one to choose the Hall thruster channel dimensions (length, inner and outer cylinder radius, inner cylinder dielectric wall thickness, outer cylinder dielectric wall thickness, channel exit region length) and physical quantities (anode voltage, cathode voltage, emission current, emitted electron energy, radial magnetic field strength, neutral number density), the resolution (number of cells in each direction) and SHRINK_FACTOR, the factor by which the size of the thruster is reduced in each dimension in the simulation.

The self-consistent electric field is solved from Poisson’s equation by the electrostatic solver in a cylindrical coordinate system. Dielectric coaxial cylinders are considered in this simulation. The simulation is performed in axisymmetric 2-D fashion.

The plasma is represented by macro-particles which are moved using the Boris scheme in a cylindrical coordinate system. Various types of elastic and inelastic collisions of the particles are calculated with the Vorpal engine’s Monte Carlo package.

## Running the simulation

After performing the above actions, continue as follows:

• Proceed to the run window by pressing the Run button in the left column of buttons.
• This simulation requires approximately 34 hours when running on four MPI cores on a modern CPU to simulate 200,000 time-steps. To view only the initial transient conditions, set Number of Steps to 1000 and Dump Periodicity to 10. Then the simulation can either be reset and rerun with the default run parameters, or by entering in the last dump into Restart at Dump Number (in this case, 100) the simulation can be restart from the chosen data dump.
• To run the file, click on the Run button in the upper right corner of the window. You will see the output of the run in the right pane. The run has completed when you see the output, “Engine completed successfully” as shown in Fig. 533.

Fig. 533 The Run Window at the end of execution.

## Analyzing the Results

If the electron density is desired the analysis script computePtclNumDensity.py may be used.

• In the leftmost panel, click the Analyze button. Select Show All Analyzers and then select computePtclNumDensity.py from the list of analyzers, then click Open at the bottom of the Analysis Controls pane.
• Enter “electrons” into the speciesName field.
• Click the Analyze button near the upper right of the Analysis Results pane.
• Repeat with other particle species if desired (“Xeplus”, “XeNeutralsGas”)

The analysis results are now viewable in the Visualize window, as shown in the following section.

## Visualizing the Results

After performing the above actions, continue as follows:

• Proceed to the Visualize window by clicking the
• Visualize* button in the leftmost panel.
• In the top of the Visualization Controls pane, switch the Data View dropdown menu to Field Analysis.
• In the Field dropdown menu, select nodalB_r to view the radial component of the magnetic field (the magnetic field is only radial). A pseudocolor plot of the potential with a radial lineout performed should be displayed as shown in Fig. 528. The magnetic field is strongest near the inner cylinder and falls off towards the outer cylinder.
• To plot the radial profile of the magnetic field at its strongest point, in the Lineout Settings section, set Intercept to “0.0005” and click Perform Lineout. If desired, select the Advanced tab to choose arbitrary start and end points for the lineout.

Fig. 534 Visualization of radial magnetic field in the cylindrical Hall thruster channel.

• To view the The background xenon neutral gas density, in the top of the Visualization Controls pane, switch the Data View dropdown menu to Data Overview.
• In the Variables section, expand Scalar Data.
• Select XeNeutralGas. A plot of the electron number density distribution will be displayed as shown in Fig. 535.

The maximum neutral gas density is set near the anode wall at the left end of the channel and decreases linearly until a minimum at channel opening at the right end of the channel.

Fig. 535 Visualization of xenon neutral gas density in the cylindrical Hall thruster channel.

To analyze the plasma sheath, plot the electric potential and particle positions by following the steps below:

• In the top of the Visualization Controls pane, switch the Data View dropdown menu to Field Analysis.
• In the Field dropdown menu, select phi to view the electric potential. A pseudocolor plot of the potential with a radial lineout performed should be displayed as shown in Fig. 536. The voltage is highest down the center of the channel.
• To plot the axial profile of the potential as shown in Fig. 536, in the Lineout Settings section, select the Horizontal tab, set Intercept to “0.00085” and click Perform Lineout. If desired, select the Advanced tab to choose arbitrary start and end points for the lineout.

In the lineout, it can be seen that the potential of the plasma bulk is approximately 310 volts. The anode voltage is set to exactly 300 volts, so the potential drop at the anode sheath is approximately 10 volts, while the potential drop at the exit sheath is the same as the bulk plasma potential.

Fig. 536 Visualization of the cylindrical Hall thruster electric potential with a line-out showing the axial sheath structure.

• In the Variables section, expand Scalar Data and select phi
• Expand Particle Data, then expand Xeplus and select Xeplus_uz to view the locations of xenon ion macroparticles colored by their axial ($$z$$) velocity.
• In the Particle Style section, set Size to 6 and Symbol to “Sphere”.
• Still under Particle Data, expand electrons and select electrons to view electron macroparticle positions monochromatically.

Plots of the electron and ion macroparticle positions overlayed on the electric potential should now be visible as shown in Fig. 537

Fig. 537 Visualization of the cylindrical Hall thruster sheath via ion and electron macroparticle positions with electric potential and ions colored according to their axial velocity.

• To plot the sputter material macroparticle locations, deselect the electrons and xenon ions, then expand BNAtoms, and select BNAtoms, as shown in Fig. 538

The sputtered material from the Hall Thruster channel can be shown by plotting the BNAtoms (red).

Fig. 538 Visualization of the sputtered material from the channel walls.

## Further Experiments

This input file can be modified to test different design parameters such as varying anode voltages, varying background neutral gas densities and varying electron emission currents. This will allow users to study high-to-low power and high-to-low throttle levels.

Also the background gas type can be changed to investigate other neutral gas kinds in this simulation set up.

A more substantial further step for a user would be to take the following steps to calculate the thrust from the device. This will require adding the history (see the code block below) to collect the appropriate data, writing a post-processing analysis script to calculate the thrust, then importing the analyzer into VSim.

• Return to the Setup window by clicking the Setup button in the leftmost panel
• Near the top of the Editor pane, click View Input File
• Scroll to the bottom of the input file and paste the following code:
<History absorbedIonVelocity>
kind = speciesAbsPtclData2
species = [ Xeplus ]
ptclAbsorbers = [ topOuterIonAbsorber rightIonAbsorber botOuterIonAbsorber ]
ptclAttributes = [ xVelocity numPtclsInMacro kineticEnergy xPosition yPosition ]
collectMethod = statsForEachStep
</History>


the collectMethod = statsForEachStep provides sums of the desired quantities in the history file. The calculation thrust would be performed in the analysis tab. Other post-run analyses can be performed in order to see a sum of where the particles are arriving, their velocity, and the creation of other figures of merit to determine the performance of the the thruster.